A precise concept of concrete geometrical category is
introduced in an axiomatic way. To any algebra L for an many-sorted
infinitary algebraic theory **T** is associated a concrete
geometrical
category **Geo**(L), the so-called classifying concrete geometrical
category of L, satisfying a universal property. The terminology
"geometrical"
is justified firstly for **Geo**(L) and secondly for any concrete
geometrical category by proving that they are all classifying ones. The
legitimate category **CGC** of concrete geometrical categories is
build up
and proved to be the dual of the legitimate category **TGC** of
topological
geometrical categories.

Keywords: concrete geometrical category, classifying geometrical category, topological geometrical category

2000 MSC: 18B99, 18F99, 18C99

*Theory and Applications of Categories,*
Vol. 14, 2005,
No. 14, pp 310-327.

http://www.tac.mta.ca/tac/volumes/14/14/14-14.dvi

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http://www.tac.mta.ca/tac/volumes/14/14/14-14.pdf

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